NON-PROJECTIVE COMPACTIFICATIONS OF $ \mathbb{C}^3 $ (IV)

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概要

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• Let $ (X, Y) $ be a smooth non-projective Moishezon compactification of $ \mathbb{C}^3 $ with $ b_2(X) = 1 $. Then $ Y $ is a non-normal irreducible divisor on $ X $ with $ K_x = -rY (r = 1, 2) $. In this paper, we mainly study the case where $ Y $ is not nef, that is, there is a curve $ C $ such that $ (Y \cdot C)_X < 0 $. First, we investigate the structure of the boundary divisor $ Y $ (Theorem 1) under the mild assumption that $ b_3(X) = 0 $. Next we define the invariant $ \delta(X) $ and compute them for the examples with non-nef boundaries (Theorems 2 and 3).

著者

• Furushima Mikio

  Department Of Mathematics College Of Education Ryukyu University

• FURUSHIMA Mikio

  Department of Mathematics Faculty of Science Kumamoto University

関連論文

• A new construction of a compactification of C^3
• Mukai-Umemura's example of the Fano threefold with genus 12 as a compactification of C^3
• NON-PROJECTIVE COMPACTIFICATIONS OF $ \mathbb{C}^3 $ (IV)

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